9 problems

Let $\mathfrak{g}$ be a semisimple Lie algebra, let $k\in\mathbf{C}$, and let $f_1,f_2$ be nilpotent elements satisfying the hypotheses of the source's Main Theorem on freeness. Le…

Let $\mathfrak{g}=\mathfrak{sp}_4$, let $f$ be a subregular nilpotent element, and let $k$ be an admissible level. Write $L(\xi^{(s)}_{i,j},\chi^{(s)}_{i,j})$ for the simple…

Minus-reduction conjecture. For any $\ta{ \kappa}\in\mathbb C$ and any V\in\operatorname{Obj}\ta{ O}_{\ta{ \kappa}},

Let ${\cal V}$ be a VOA corresponding to a four-dimensional ${\cal N}=2$ SCFT, and let DS reduction produce another VOA corresponding to a four-dimensional ${\cal N}=2$ SCFT. Denot…

Kac–Roan–Wakimoto–Arakawa conjecture. The functor $\Psi_f^-$ is exact, and the image of every simple module is either simple or zero. Moreover,

Let $\mathfrak{g}$ be a Lie algebra, let $f$ be a nilpotent element of $\mathfrak{g}$, and let $L_k(\mathfrak{g})$ be the simple affine vertex algebra at level $k$. Let…

Let $\mathfrak{g}$ be a Lie algebra, let $\widehat{\mathfrak g}$ be its affine algebra, let $d_{st}$ be the standard semi-infinite cohomology differential, let $\sigma^\lambda$ be…

Free-field realization conjecture. In the Lie-algebra case, $\mathrm{W}$ should be isomorphic to the corresponding W-algebra, namely the Hamiltonian or quantum Drinfeld–Sokolov red…

qDS reduction conjecture. The chiral algebra associated to the class $\mathcal{S}$ theory with a puncture of type $\Lambda$ is obtained by performing qDS reduction with respect to…